Session: 12-22-01: Multiscale Models and Experimental Techniques for Composite Materials and Structures

Paper Number: 138290

138290 - An Adaptive Manifold- and Discrete Empirical Interpolation Method-Based Reduced Order Model for Nonlinear Solids. 

Predicting the multiscale behavior of heterogeneous nonlinear materials is critical to many engineering fields but requires computationally intensive techniques such as computational homogenization. Reduced-order models have been developed to address the demand for multiscale modeling, but thus far most are limited to single-scale or linear behavior.

            In this work, we propose a novel form of reduced-order model for emulating multiscale processes in heterogeneous materials. This technique bypasses much of the computational effort induced by multiple scales while also accounting for inherent physical nonlinearities, both geometric and material. The reduced-order model is constructed within a computational homogenization framework, with computational savings achieved at the finest scale, seeing as it is the source of most of the simulation work. Computational homogenization relies on the solution of nonlinear Partial Differential Equations (PDEs) at the micro-scale that are for irreversible processes coupled with nonlinear Ordinary Differential evolution Equations (ODEs), which describe material behavior. PDE reduction for geometric nonlinearities is accomplished using a Manifold-based Reduced Order Model (MNROM) which can interpolate microscopic fields from principal components. ODE reduction for material nonlinearities is accomplished using the Adaptive Discrete Empirical Interpolation Method (ADEIM) with goal-oriented sampling, which can project evolving field data globally from a few locally modeled points. Both PDE and ODE schemes are joined together using operator splitting to tackle coupled problems. 

            We demonstrate our coupled reduced order model by examining elasto-viscoplastic behavior of particulate composites with a nearly incompressible binder. This is done in two-dimensions for a reasonably complex microstructure, considering large strains and large plastic deformations. We provide several statistical examples to verify coverage of the plastic loading envelope, with further in-depth examination of tailored engineering problems. 

Presenting Author: Karel Matous University of Notre Dame

Presenting Author Biography: Dr. Matouš is a Professor of Aerospace and Mechanical Engineering at the University of Notre Dame. He received his M.S. and Ph.D. in Theoretical & Applied Mechanics from the Czech Technical University in Prague. Dr. Matouš served as the Director of the Center for Shock Wave-processing of Advanced Reactive Materials (C-SWARM), which was established as one of the six NNSA Centers of Excellence whose primary focus had been on the emerging field of predictive science. In 2016, he held a visiting professor position at the Department of Mechanical Engineering at the Eindhoven University of Technology. Dr. Matouš’ interests are in predictive computational science and engineering at multiple spatial and temporal scales, including multi-physics interactions, the development of advanced numerical methods, and high-performance parallel computing. His research focuses on the interplay between applied mathematics, computer/computational science, and physics/materials science. Moreover, he leads a research program in image-based (data-driven) modeling of heterogeneous systems, focusing on co-designed simulations and experiments based on statistical analysis, computational mathematics, and AI/machine learning. He has authored or co-authored more than 200 journal and/or conference proceedings articles and abstracts. He is involved in several interdisciplinary research programs with funding from various agencies and private companies. In 2022, Dr. Matouš received the Rev. Edmund P. Joyce, C.S.C. Award for Excellence in Undergraduate Teaching from the University of Notre Dame. Moreover, Dr. Matouš received the Rector's Award for the best Ph.D. students from the Czech Technical University in Prague. Several articles from Dr. Matouš’ group have been featured on the Web of Science’s highly cited list. One of his papers appeared as the cover article in Proceedings of the Royal Society A. He is a member of ASME, SES, USACM, EUROMECH, and IACM. Dr. Matouš is a Fellow of ASME. Dr. Matouš serves as an Associate Editor of the Journal of Computational Physics and International Journal for Multiscale Computational Engineering.

Authors:

Karel Matous University of Notre Dame
Zachariah El-Hajj University of Notre Dame